Preheat the oven to 350°F (175°C). Roll out the pie crust on a floured surface and fit it into a 9-inch pie pan, trimming the edges as needed. Crimp the edges decoratively and set aside.
In a mixing bowl, combine sugar, corn syrup, and salt. Whisk together until fully blended, creating a smooth, lucent mixture.
Add the eggs, one at a time, to the sugar mixture, whisking after each addition until the mixture becomes thick and slightly frothy.
Stir in the melted butter, vanilla extract, and a pinch of salt; mix until the filling is smooth and shiny.
Sprinkle half of the pecan halves evenly over the bottom of the pie crust. Pour the filling gently over the pecans, spreading to distribute evenly.
Arrange the remaining pecan halves on top of the filling in a decorative pattern. Place the pie on the middle rack and bake for 50 minutes, or until the filling is set and the top is golden brown with toasted pecans.